Thermal Conductivity of Aluminum Scandium Nitride for 5G Mobile Applications and Beyond Yiwen Song, Carlos Perez, Giovanni Esteves, James Spencer Lundh, Christopher B

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Thermal Conductivity of Aluminum Scandium Nitride for 5G Mobile Applications and Beyond Yiwen Song, Carlos Perez, Giovanni Esteves, James Spencer Lundh, Christopher B. Saltonstall, Thomas E. Beechem, Jung In Yang, Kevin Ferri, Joseph E. Brown, Zichen Tang, Jon-Paul Maria, David W. Snyder, Roy H. Olsson III, Benjamin A. Griﬃn, Susan E. Trolier-McKinstry, Brian M. Foley, and Sukwon Choi*

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ABSTRACT: Radio frequency (RF) microelectromechanical systems (MEMS) based on Al1−xScxN are replacing AlN-based devices because of their higher achievable bandwidths, fi fi suitable for the fth-generation (5G) mobile network. However, overheating of Al1−xScxN lm bulk acoustic resonators (FBARs) used in RF MEMS filters limits power handling and thus the phone’s ability to operate in an increasingly congested RF environment while maintaining its maximum data transmission rate. In this work, the ramifications of tailoring of the piezoelectric fi response and microstructure of Al1−xScxN lms on the thermal transport have been studied. fi − −1 −1 The thermal conductivity of Al1−xScxN lms (3 8Wm K ) grown by reactive sputter deposition was found to be orders of magnitude lower than that for c-axis-textured AlN films due to alloying effects. The film thickness dependence of the thermal conductivity suggests that higher frequency FBAR structures may suffer from limited power handling due to exacerbated overheating concerns. The reduction of the abnormally oriented grain (AOG) density was found to have a modest effect on the measured thermal conductivity. However, the use of low AOG density films resulted in lower insertion loss and thus less power dissipated within the resonator, which will lead to an overall enhancement of the device thermal performance. KEYWORDS: aluminum scandium nitride, frequency-domain thermoreflectance, thermal conductivity, time-domain thermoreflectance, phonon transport, radio frequency acoustic filters, scandium aluminum nitride

1. INTRODUCTION counter signal attenuation. Higher power and smaller size fl To meet the ultrawide bandwidth requirements for fifth- translate into an increased operational heat ux. This higher 1,2 fl generation (5G) mobile phones, manufacturers have heat ux, meanwhile, occurs within a solid solution Downloaded via PENNSYLVANIA STATE UNIV on May 14, 2021 at 19:14:22 (UTC). − recently adopted scandium aluminum nitride (Al1−xScxN; x (Al1 xScxN) that will have a greatly reduced thermal is the Sc composition), a wurtzite-structured solid solution, as conductivity relative to the AlN material that it replaces. See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. the piezoelectric in film bulk acoustic resonators (FBARs). The Furthermore, the FBAR structure itself is prone to overheating interest in replacing aluminum nitride (AlN) FBARs [used in because the piezoelectric film is typically released from the some 4G mobile phone radio frequency (RF) duplexers] with substrate, which severely limits the thermal pathway for heat Al1−xScxN FBARs originates from the enhancement of dissipation. Al1−xScxN resonators exhibit a 50% larger resonant 2 10 electromechanical coupling (kt ), which scales indirectly with frequency drift with temperature rise than their AlN ffi − 11,12 the piezoelectric coe cient d33. The d33 of ScxAl1 xN has been counterparts. Self-heating in ScxAl1−xN FBARs can, in predicted to reach a value five times larger than that for AlN at 3 principle, constrain the maximum transmission rate, and if x =0.43. This dramatic enhancement of d33 and the allowed to proceed unchecked, may cause thermal failure.7,12,13 complementary metal-oxide-semiconductor (CMOS) process- Despite the thermal implications on performance, fundamental compatibility facilitates the development of 5G mobile phone − − duplexers1,4 6 with wide bandwidth7 9 and low insertion loss.7,8 These intrinsic advantages are, in turn, motivating Received: February 11, 2021 fi 2 Accepted: April 2, 2021 signi cant research aimed at achieving high kt and quality factor (Q), simultaneously. Published: April 14, 2021 However, for an FBAR to handle the high operational frequencies of the 5G mobile network, its physical dimensions typically decrease, and higher RF input powers are required to

fi fi × Figure 1. (a) TEM cross-section of an Al0.875Sc0.125N lm showing AOGs and their propagation through the lm thickness. (b) 75k and (c) × fi 200k plan-view SEM images of an Al0.8Sc0.2N lm showing the primary c-axis-oriented grain structure as well as AOGs. (d) 750 nm thick fi fi fi Al0.8Sc0.2N lm with a high density of AOGs, and (e) inverse-pole gure, gathered from EBSD, that maps the orientation of AOGs from the lm normal direction (Z-direction). EBSD results show no strong preferred orientation for the AOGs.

fi Figure 2. (a) Background subtracted Raman spectra of AlN, Sc0.125Al0.875N, and Sc0.2Al0.8N lms. The dashed lines qualitatively show the redshift of fi the E2 (high) and A1 (LO) modes as the Sc content in the lms is increased. (b) Shift of the E2 (high) phonon frequency (peak position) as a 21 function of the Sc content from this study and Deng et al. (c) Shift of the A1 (LO) phonon frequency as a function of the Sc content from this study, Deng et al.,21 and Mock et al.22 investigations of the thermal transport processes that govern 2. RESULTS AND DISCUSSION heat dissipation in Al − Sc N remain lacking. 1 x x 2.1. AlN and Al1−xScxN Film Description. Polycrystalline In response, this work reports how changes in the alloy fi AlN and Al1−xScxN lms with compositions of x = 0, 0.125, composition, thickness, and microstructure influence the and 0.20 were deposited via reactive sputter deposition on 6″ fi ⟨ ⟩ thermal conductivity of Al1−xScxN. Speci cally, we measure Si 100 substrates using pulsed-DC magnetron sputtering, 14 the variation in Al − Sc N thermal conductivity for films following previous reports. Deposition conditions for the 1 x x fi synthesized via reactive sputter deposition as a function of Sc Al1−xScxN lms were 5 kW of power on the single-alloy target, fl composition, film thickness, temperature, and the concen- an Ar/N2 gas ow of 25/125 sccm, and a platen temperature of 375 °C. For AlN growth, a platen temperature of 350 °C and tration of abnormally oriented grains (AOGs). Through this fl fi ff an Ar/N2 gas ow of 20/80 sccm were employed. The lm examination, the design trade-o s associated with this material, stress was controlled using substrate bias, which applies RF in terms of attempting to optimize both the device acousto- power to the substrate during deposition to increase the electric performance and the ability to dissipate heat, are compressive stress of the film.15,16 The film thickness range identified. In particular, it is shown that several phonon used in this study was 50−1000 nm, while the stress ranged scattering mechanisms associated with solid solution (i.e., from −1700 to −5.7 MPa. These stress values were 17 phonon-alloy/disorder scattering), grain boundaries, and film determined via wafer curvature measurements. As reported elsewhere, the density of AOGs tended to be lower in films surfaces drive a substantial thermal conductivity reduction with higher substrate bias.18 relative to AlN. Device engineers must therefore grapple with Figure 1 shows representative transmission electron the necessity of designing cooling solutions enabling the use of − − microscopy (TEM) and scanning electron microscopy a low thermal conductivity material (<10 W m 1 K 1) (SEM) images. As shown in Figure 1c, the columnar grain fi operating within the envelope of 5G requirements. size of the c-axis-textured AlN and Al1−xScxN lms were

19032 https://doi.org/10.1021/acsami.1c02912 ACS Appl. Mater. Interfaces 2021, 13, 19031−19041 ACS Applied Materials & Interfaces www.acsami.org Research Article approximately 35 nm across in all samples. The AOGs nearly 4. Reductions in the scattering time of phonons, in turn, fi − observed in the Al1−xScxN lms had lateral sizes of 50 250 imply a lessening in the thermal conductivity. nm. The degree of c-axis orientation was characterized with X- 2.2. Thermal Characterization Results. Thermal con- ff ray di raction by measuring the rocking curve of the {0002} ductivity measurements of c-axis-textured AlN and Al1−xScxN fl fi fi re ection of the Al1−xScxN lm. Correlation between the lms with various Sc compositions (x = 0.125 and 0.2) and rocking curve measurement of various AlN films and the two different thicknesses (∼110 and ∼760 nm) were ffi 2 fl 25 electromechanical coupling coe cient (kt ) has shown that performed using time-domain thermore ectance (TDTR) films with smaller rocking curve linewidths (full width at half- and frequency-domain thermoreflectance (FDTR) techni- 2 19 26 maximum, FWHM) exhibit high kt . Therefore, Al1−xScxN ques. This cross-validation was conducted to rule out films with rocking curve measurements ≤2° should be used to potential sources of error and reduce uncertainty due to the 2 20 fi 27 achieve high kt . In this study, lms with a thickness greater complementary sensitivities of the two techniques. ° than 400 nm showed a FWHM less than 2 . As shown in Figure 3a, for Al1−xScxN with x = 0.125 and 0.2 The presence of AOGs lowers the crystallographic texture of and a film thickness of ∼760 nm, the measured cross-plane fi −1 −1 Al1−xScxN lms. Figure 1c illustrates AOGs on the Al0.8Sc0.2N thermal conductivities (κ) were ∼7.4 and ∼4.8 W m K , fi lm that protrude out of the c-axis-oriented matrix. As shown respectively (the actual thicknesses for the AlN, Al0.875Sc0.125N, in the electron backscattering diffraction (EBSD) data (Figure and Al Sc N films are 733, 765, and 816 nm, respectively, as fi 0.8 0.2 1e) of Figure 1d, for an Al0.8Sc0.2N lm with a high density of measured by spectroscopic ellipsometry). These values are an AOGs, there is no preferred orientation for the AOGs. order of magnitude lower than that for the AlN film with a Raman spectroscopy was employed to qualitatively assess similar thickness and microstructure (∼51 W m−1 K−1) and 2 changes in the phonon energies and scattering rates that were orders of magnitude lower than a single-crystal epitaxial film of induced with the incorporation of scandium. Using this AlN (∼320 W m−1 K−1).28 It should be noted that the average approach, Figure 2a presents the difference in Raman spectra columnar (lateral) grain size resulting from the reactive sputter 18,29 between the Si wafer coated with Al1−xScxN and the bare Si deposition process was consistent (∼35 nm; Figure 1c) − fi substrate where modes associated with the E2 (high) (635 among all the AlN and Al1−xScxN lms investigated in this −1 − −1 660 cm ) and A1(LO) (825 850 cm )ofAl1−xScxN are work. Consequently, from a practical perspective, the clearly observed. The incorporation of scandium causes a reduction in thermal conductivity underscores the intrinsic redshift and broadening of the Raman modes indicating a trade-off between piezoelectric and thermal performance in the softening of the lattice and an increased scattering rate of the Al1−xScxN solid solution. κ optical phonons. Each change is associated with a reduction in This large reduction in in moving from AlN to Al1−xScxN thermal conductivity. Softening, for example, is seen in the films is attributed to increased phonon scattering that is 30 redshift of the E2 (high) and A1 (LO) mode peak positions to primarily due to phonon-alloy disorder scattering. The lower wavenumbers with additional Sc content (Figure 2a). significantly increased phonon scattering rate is also manifested Figure 2b,c quantifies the concentration-dependent shift, which by the broadening of the linewidth of the Raman active 21 is similar to those reported previously by Deng et al. and phonon modes of the Al Sc N and Al Sc N films 22 0.875 0.125 0.8 0.2 Mock et al. Phenomenologically, Sc incorporation promotes compared to those for AlN, as shown in Figure 2 and Table softening because the average atomic mass of the oscillators 1.24,31 21 ff ff κ increases and the bond covalency drops. Both e ects reduce Alloying has an acute e ect on the of Al1−xScxN because of thermal conductivity. the lattice disruption associated with alloying AlN (wurtzite) κ ∼ The scattering rate of the optical modes increases with Sc with ScN (rocksalt). To quantify, the of Al0.8Sc0.2N( 4.8 W −1 −1 ∼ ∼ content as well, as indicated by the broadening of the Raman m K )is 36% lower than that of Al0.875Sc0.125N( 7.4 W modes in Figure 2a with additional scandium. Quantitatively, m−1 K−1) for films with a thickness of ∼760 nm. In contrast, as shown in Table 1, the linewidth of the E2 (high) mode previous work examining the wurtzite phase isostructural alloy Al1−xGaxN with identical characterization methods found that Table 1. Peak Position and Linewidth (FWHM) of the E2 a similar reduction in κ (35%) required a much larger variation ∼ − 32 (High) Phonon Mode of ScxAl1−xN Films with 730 820 in composition from x ∼ 0.1 to ∼0.5. Mechanistically, the b a κ nm Thicknesses large reduction in the of Al1−xScxNascomparedto Al − Ga N can be attributed to the evolution in bond Sc content [%] 0 (AlN) 12.5 20 1 x x characteristics33 of the solid solution with increasing x. peak position [cm−1] 657.1 ± 0.4b 643.2 ± 1.8b 635 ± 2.1b c c c Increasing x in Al1−xScxN solid solutions results in an increased 658 628.9 611.4 displacement of the Al/Sc atoms along the c-axis.33 This results 657d ff −1 b b b in a reduction of the elastic sti ness constant C33 and a FWHM [cm ] 15.6 52.3 61.5 nonlinear enhancement of the piezoelectric stress constant a Data reported in this study were based on an average of 100 e .4,34 Accordingly, as Sc content approaches the critical b c fi 33 measurements. This study. Calculated using linear t parameters concentration x at which phase separation occurs, significant reported by Deng et al.21 dValue reported for unstrained AlN at 300 c 24 increases are observed in both the piezoelectric modulus d33 K. ∼ ffi 2 ( e33/C33) and the electromechanical coupling coe cient kt 2 2 ε ε 4 11 (=e33 /[(C33 + e33 / 33) 33]. The lattice softening with increases with increasing Sc content from 15.6 cm−1 for AlN to increasing x lowers the group velocities of the acoustic −1 κ 61.5 cm for Al0.8Sc0.2N. This suggests much more disruption phonons that dominate . Thus, it is anticipated that Al1−xScxN in the period potential due to solid solution. Owing to the (in the wurtzite phase) will continue to exhibit a nonlinear − 23 κ time uncertainty relation, in which scattering time is reduction in as x approaches xc, whereas d33 is maximized. inversely proportional to FWHM, this implies a reduction of Despite being dominated by alloy scattering, size effects are the scattering time of the optical phonon modes by a factor of also evident in the thermal response of the Al1−xScxN. As

19033 https://doi.org/10.1021/acsami.1c02912 ACS Appl. Mater. Interfaces 2021, 13, 19031−19041 ACS Applied Materials & Interfaces www.acsami.org Research Article

Figure 3. (a) Compositional dependence of Al1−xScxN thermal conductivity obtained from TDTR/FDTR measurements and virtual crystal “ ” approximation (VCA) simulation (to be discussed in the Thermal Modeling Results section). (b) Evolution of the piezoelectric modulus d33 ﬀ (from ref 35) and elastic sti ness constant C33 (from ref 34).

ﬁ ﬁ Figure 4. (a) Thickness dependence of the thermal conductivity of Al0.8Sc0.2N lms. (b) Residual stress in the two series of the Al0.8Sc0.2N lms (low stress vs high stress) as a function of layer thickness (to be discussed in the “Thermal Modeling Results” section).

∼ fi Figure 5. (a) Temperature-dependent thermal conductivity of the 760 nm thick Al1−xScxN(x = 0.125 and 0.2) lms. (b) Also shown is the AlN film thermal conductivity as a function of temperature. shown in Figure 3a, κ is observed to decrease over all Sc a noticeable thickness dependence of the cross-plane κ for fi ∼ fi fi κ fi compositions as the thickness of the lms decreases from 760 these Al0.8Sc0.2N lms; speci cally, plateaus for lm ∼ to 110 nm (the actual thicknesses for the AlN, Al0.875Sc0.125N, thicknesses >400 nm and decreases with decreasing thick- fi κ and Al0.8Sc0.2N lms are 157, 107, and 105 nm, respectively). nesses <400 nm. The turnover in near 400 nm, as shown in When the film thickness of a crystallite becomes comparable to Figure 4a, implies that there is an appreciable amount of heat the mean-free path of phonons, incoherent phonon-boundary being carried by phonons with mean-free paths on this order.40 scattering will impact κ.36,37 Since these are sputtered films, it As the thickness of the films drops below 400 nm, these is also speculated that the first 20−50 nm of the film where the phonons begin to scatter at the boundaries with increasing c-axis growth has not completely taken over may be partly frequency, leading to a continuing reduction in κ as the responsible for the observed thickness dependence of the κ. thickness decreases further. On the other hand, the composi- Recognizing that film thickness is a main design parameter tional disorder and grain boundaries reduce κ via scattering of that determines the resonant frequency of FBARs,38,39 the film shorter wavelength phonons. Thermal management strategies ff 36,37 fi thickness e ect on the thermal conductivity of Al1−xScxN will therefore be necessary when sub-micron thickness lms are was investigated in more detail via TDTR measurements to integrated into FBAR structures to realize GHz-range better understand the trends observed in Figure 3a. For this resonators.41 fi ff reason, a series of Al1−xScxN lms with the thickness range of The implicit nature of thermal e ects is further underscored 50−1000 nm at a fixed composition (x = 0.2) and consistent by examining the temperature-dependent thermal conductivity ∼ fi lateral grain size ( 35 nm) were synthesized. Figure 4a shows of the thicker Al0.875Sc0.125N and Al0.8Sc0.2N lms (765 and 816

19034 https://doi.org/10.1021/acsami.1c02912 ACS Appl. Mater. Interfaces 2021, 13, 19031−19041 ACS Applied Materials & Interfaces www.acsami.org Research Article nm thick, respectively) over the ambient temperature range of AOGs is on the order of hundreds of nanometers, their density − − 100 450 K, along with data from 300 450 K for the 733 nm within the majority of the Al1−xScxN matrix remains relatively AlN film (Figure 5). Like most crystalline solids, as the low. As a result, the rate at which phonons scatter with these temperature is increased beyond 300 K, the thermal AOG interfaces does not impede the total flow of heat carriers conductivity of AlN monotonically decreases because more to a greater extent than the other scattering mechanisms 42 κ fi frequent Umklapp scattering processes cause the phonon present. That is, the overall cross-plane of the ScxAl1−xN lms mean free paths, and thus the thermal conductivity, to is relatively invariant to the AOG number density. Con- decrease. In contrast, a negligible reduction in κ with increasing sequently, while the presence of AOGs in Al1−xScxN is critical temperature is observed for the Al0.875Sc0.125N and Al0.8Sc0.2N for optimizing the electro-acoustic performance of RF MEMS films, as shown in TDTR measurement results listed in Figure resonators, their impact on thermal transport is observed to be 5. A similar trend was found in a previous work on Al1−xGaxN minimal for AOG densities that are low enough to allow the films with x = 0.3 and 0.7.32 films to be piezoelectrically functional. Scattering mechanisms 30 Given that these temperatures are well below the Debye associated with alloying and the fine crystallite structures 48,49 temperatures of the two constitutive materials,43,44 the (lateral grains; ∼35 nm) of the c-axis-textured films saturation of κ indicates that the increase in heat capacity is dominate (i.e., restrict) the κ. To this end, reduction of the balancedbut not overwhelmed by increases in scattering AOG density should not be expected to improve the material’s with temperature. This, in turn, suggests that heat transport is thermal conductivity. However, lower insertion loss associated not being dominated by phonon−phonon (i.e., Umklapp) with minimizing AOG density will result in lower power fi scattering but instead other scattering mechanisms including dissipation within the resonator. Therefore, lms with low fi those discussed so far (grain boundary, film surface, alloy- AOG density will be still bene cial in terms of enhancing the disorder scattering, etc.). device thermal performance. 2.3. Thermal Modeling Results. A computational study Finally, thermal conductivity was examined as the Al1−xScxN microstructure was purposely altered by intentionally varying was performed to understand the physical mechanisms driving ff AOG45 densities for films having a fixed composition (x = 0.2) the FBAR design trade-o s, as they relate to thermal transport, ∼ recognizing that composition,30 film thickness,36,37 and the fine and thickness ( 760 nm). Control of AOG density was 48 realized through incomplete conditioning of the target and lateral grain size each contribute to the reduction in the chamber combined with incomplete purging of the deposition thermal conductivity of Al1−xScxN with respect to the base AlN chamber and load lock. This process keeps the reactive sputter (x = 0) and ScN (x = 1) crystals. Ultimately, it was found that deposition46 conditions constant while varying the AOG the transport mechanisms in these textured (one-dimensionally 18,33,35 oriented) films differ from other epitaxial (i.e., three-dimen- density. The inclusion of AOGs in Al Sc − N films can x 1 x sionally oriented) isostructural wide band gap alloys such as dramatically increase the surface roughness in AlxSc1−xN fi 32 materials with high Sc content, thus potentially lowering the AlxGa1−xN lms. This is because the sputter growth Q factor of RF microelectromechanical system (MEMS) conditions employed lead to close-packed vertically aligned columnar grains which play a significant role in the behavior of resonators. Recent reports in the literature demonstrate the phonons and in turn thickness, temperature, and composition significance of the microstructural quality of the base trends of the measured thermal conductivity. Al − Sc N film. For example, bulk acoustic wave (BAW) 1 x x In the previous section, thermal conductivity measurements resonators realized in nearly AOG-free Al Sc N films have 0.72 0.28 were performed as a function of the ScN composition, film exhibited an effective k 2 of 16% and a Q of 1070 at 3.5 t max thickness, temperature, and AOG density. These results were GHz.47 analyzed under the paradigm of the phonon gas model The effect of the AOG is minimal, however, from a thermal 50,51 leveraging the VCA, to assess the comparative importance perspective. The cross-plane κ is only minimally impacted by ff κ of the relevant scattering e ects on the thermal conductivity of the density of AOGs, as shown in Figure 6. The of Al0.8Sc0.2N fi Al1−xScxN. The model is in no way prescriptive as the phonon lms with varying levels of AOGs were measured using TDTR gas model is itself questionable when examining solid at room temperature. The qualitative number density of the solutions.52 However, it is used here to compare various AOGs is shown in the SEM images (insets) in Figure 6. effects owing to its ease of implementation in a way consistent Despite the fact that the characteristic size of the individual with decades of previous research.53 Practically, the thermal conductivity was modeled using the k-space phonon gas model

π/a ℏω ω eff jj()kfd( (), kT ) 22 κ = ∑ ∫ 2 τω((),)()jjkTvkk j 0 6π dT dk (1) ω where is the angular frequency, k is the wave vector, aeff is the Debye lattice constant, ℏ is the Planck constant divided by π 2 , kB is the Boltzmann constant, T is the temperature, v is the group velocity, df/dT is the temperature derivative of the Bose−Einstein distribution, and the summation is over the j- ﬁ ﬀ Figure 6. Thermal conductivity of Al0.8Sc0.2N lms with varying levels dispersion branches. The e ective lattice constant, aeff, was of AOG density. The insets are 75k× SEM images that qualitatively calculated by assuming a spherical unit cell where the volume show the increasing AOG density as moving to the right of the x-axis. of the sphere is equal to the volume of the real unit cell. Since

19035 https://doi.org/10.1021/acsami.1c02912 ACS Appl. Mater. Interfaces 2021, 13, 19031−19041 ACS Applied Materials & Interfaces www.acsami.org Research Article the measured cross-plane κ is dominated by energy transport temperature-dependent AlN thermal conductivity.60 The AlN fi along the c-axis, aeff was assumed to be equal to the c lattice lms investigated in this work are composed of vertically constant (0.498 nm). The total scattering rate, 1/τ, was oriented columnar nano-grains, as shown in Figure 1a−c. The calculated using Matthiessen’s rule to sum the contributions grain boundaries significantly increase scattering, causing these τ ω2 − fi from Umklapp scattering, 1/ U = B exp( C/T), intrinsic lms to exhibit a much lower thermal conductivity than τ ω4 τ − 60 ff impurity scattering, 1/ I = A0 , alloy scattering, 1/ A = x(1 epitaxial AlN. The e ective grain size was, therefore, deduced ω4 τ fi x)A , boundary scattering, 1/ B = v/dfilm, and grain boundary by adjusting the model to t experimental measurements of τ ff − scattering, 1/ G = v/dgrain, where x is the ScN fraction, dfilm is this work. This resulted in an e ective grain diameter of 70 fi ff the lm thickness, and dgrain is the e ective grain size. Deduced 170 nm, which is much larger than the measured 35 nm. scattering rate coefficients are presented in Table 2. However, the overprediction is consistent since the grains are columnar with a 35 nm diameter and lengths equal to the film − Table 2. Scattering Coefficients Obtained by Fitting the thickness (50 1000 nm), and eq 1 assumes isotropic/spherical VCA Model with Experimental Data grains, making the effective grain size larger than the grain diameter. The alloy scattering coefficient was then determined scattering coefficient value units by fitting to the composition-dependent data. The alloy B 1.22 × 10−19 s scattering term was forced to be constant between both the fi C 290 K thickness and composition series of the Al1−xScxN lms. The × −47 3 A0 4 10 s impact of AOG scattering was neglected since no AOG density A 5.5 × 10−42 s3 dependence was found, as shown in Figure 6. Figure 3a plots the composition-dependent model for two fi ∼ ∼ This model assumes that the dispersion, thermal con- lm thicknesses (dfilm = 125 and 750 nm) along with ductivity, and grain geometries are isotropic. The impact of experimental results. It was not possible to fit the composition these assumptions will be discussed in more detail later. trend of both thicknesses simultaneously. This is because the Previous studies have shown that dispersion assumptions can effective grain size is not constant with film thickness. As the have significant effects on thermal predictions.54,55 Therefore, a thickness of the films increases, so does the height of the full dispersion was used in the model.56 However, since AlN columnar grains (not the lateral grain diameter), leading to an ff ff and ScN possess di erent crystal structures, wurtzite and increase in the e ective isotropic grain diameter, dgrain (it rocksalt, it is not possible to average the dispersions in should be noted that the TDTR and FDTR experiments examining the solid solution. Instead, AlN was assumed to act probed the cross-plane κ values). Therefore, the model ff as a host material for Sc impurities. This approximation has predictions shown are for two di erent grain sizes (dgrain = shown to be valid when modeling Al1−xScxN optical properties 70 and 170 nm) in the thin (dfilm = 125 nm) and thick (dfilm = 22 fi up to Al0.8Sc0.2N. However, the elastic constant, C33, 750 nm) composition series which t the experimental results significantly softens with alloying, as shown in Figure 3b, well. leading to significant changes in the maximum phonon The effect of changing isotropic grain size with film frequency and sound speed. This was accounted for by scaling thickness is observed in the thickness-dependent data. Figure fi κ the dispersion, and in turn the velocities, using the ratio of 4a plots the lm thickness dependence of the of Al0.8Sc0.2N longitudinal velocities predicted from the elastic constants films. Below 400 nm thickness, the κ rapidly rises due to plotted in Figure 3b boundary scattering of the finite thickness film. Above 400 nm, the conductivity plateaus and becomes thickness independent. vx() Cx()(0)ρ fi L = 33 It should be noted that for epitaxial GaN lms, the thickness vL(0) Cx33(0)ρ ( ) (2) dependence was shown to extend into tens of micron thicknesses where the film becomes bulk.61 The low thickness ρ where vL(x)and (x) are the composition-dependent plateau in this case originates from the grain boundaries taking longitudinal velocity and density, respectively. The mass over as the dominant scattering mechanism for long wave- ρ density (x)ofScxAl1−xN was calculated based on the unit length, long mean-free path phonons (i.e., Debye-like acoustic cell volume (V) and the molecular weight (M) as a function of modes). the Sc composition, x. The lattice parameters of the wurtzite The model is plotted for the two grain sizes (dgrain = 70 and ScxAl1−xN have been reported in ref 57, and the corresponding 170 nm) used in the composition data to show the impact of a and c values for x = 0, 0.125, and 0.2 were extracted via linear grain boundary scattering (Figure 4a). The two grain sizes interpolation to calculate the unit cell volume. The molecular plotted bound the data above 100 nm thickness since the low − weight of ScxAl1−xN is calculated as M = xMScN +(1 x)MAlN. film thicknesses have small effective grains. However, as the Finally, the density is calculated using film thickness increases, the grain length and its effective size ZM() x increase and approach the 170 nm limit. This hypothesis is ρ()x = further supported since the 50 nm thick films fall below the NV (3) bound indicating that the effective grain sizes in this case are where Z is the number of molecules per unit cell and N is smaller than 70 nm. ’ ff Avogadro s number. The calculated mass density of ScxAl1−xN Additionally, Figure 4a suggests that the e ective grain sizes 3 was 3.24, 3.28, 3.31, and 4.24 g/cm for x = 0, 0.125, 0.2, and of the anomalous composition data point, thick Al0.8Sc0.2N 1, respectively. It should be noted that experimentally shown in Figure 3a, is smaller than the rest of that series. The ρ ρ 58 3 59 determined AlN and ScN are 3.23 and 4.25 g/cm , thickness-dependent plot is for the 20% Sc composition, which respectively. is shown in Figure 3a to not be predicted by the composition Umklapp and intrinsic impurity scattering coefficients were trend. Many of the films with thicknesses near 750 nm fall determined by fitting the model to previously reported between the 70 and 170 nm bound in Figure 4a indicating a

19036 https://doi.org/10.1021/acsami.1c02912 ACS Appl. Mater. Interfaces 2021, 13, 19031−19041 ACS Applied Materials & Interfaces www.acsami.org Research Article true effective grain size closer to 115 nm. This may suggest that and possibly stress, among other factors, complicating the grain size has some composition dependence; therefore, 115 phonon physics. Therefore, a more rigorous model for these nm grain size was used in the temperature plot of the films needs to be developed, in order to properly describe the Al0.8Sc0.2N, as shown in Figure 5a. anisotropic phonon transport and accurately predict thermal In addition to the thickness dependence, two sets of data are conductivity. plotted in Figure 4b to show the effect of residual film stress. The two sets were grown with different substrate bias, leading 3. CONCLUSIONS to a film set with higher levels of compressive stress and a film This work investigated the physics of thermal transport that set with lower levels of compressive stress (Figure 4b). It governs the thermal conductivity of Al − Sc N, a fundamental should be noted that a higher substrate bias leads to films with 1 x x building block for 5G RF MEMS. The thermal conductivities higher levels of compressive residual stress. These stress values of c-axis-textured Al − Sc N films were found to be 1 order of were determined via wafer curvature measurements.17 1 x x magnitude lower than similarly textured polycrystalline AlN Consistently, the films with lower stress have a higher κ. films and 2 orders of magnitude lower than single crystal and/ Currently, it is unclear by what mechanism stress impacts or bulk AlN. This abrupt reduction of thermal conductivity thermal conductivity. There are multiple potential ways in with the incorporation of Sc atoms into the AlN crystal can be which there could be coupling between the average stress state understood in terms of phonon-alloy/disorder scattering, in of the film and thermal conductivity. These will be discussed in the context of the phonon gas theory. Increasing the Sc more detail in a follow-on publication but are introduced composition results in a further decrease in the thermal briefly here. First, a compressive biaxial in-plane stress could conductivity due to structural frustration and lattice softening, lead to either a change in the N−Al−N bond angle and/or ff 62 which is an e ect absent in isomorphs such as Al1−xGaxN. A increased out-of-plane (cross-plane) bond length. These relatively strong film thickness dependence of the thermal factors, in turn, reduce group velocities and increase conductivity was observed for the Al − Sc N films. The anharmonicities, resulting in a reduced cross-plane thermal 1 x x Al − Sc N exhibited a weak temperature dependence beyond conductivity. Second, changes in stress are often accompanied 1 x x fi ff room temperature and 450 K. The impact of AOGs on the by changes in the lm microstructure. This, in turn, a ects the cross-plane thermal conductivity was found to be negligible for contribution of grain scattering to the effective phonon mean- fi the piezoelectrically functional Al1−xScxN lms tested in this free path. Third, under energetic bombardment conditions work. associated with sputter growth (especially with a biased Outcomes of this work support the necessity of electro- substrate), atomic peening can induce densification of grain thermo-mechanical co-design of 5G Al1−xScxN-based RF boundaries, embed sputter gas atoms, and induce point fi 63 acoustic lters. From a thermal standpoint, for Al1−xScxN- defects. The latter two would be expected to degrade based BAW filters, the solidly mounted resonator configuration crystallinity and hence thermal conductivity. Furthermore, if fl would be preferred over the FBAR (free-standing membrane) the deposition rate is altered by the factors that in uenced the configuration due to the poor thermal conductivity of stress state, it should be noted that as the growth rate rises, the Al1−xScxN. The thermal property data set generated in this concentration of defects also tends to increase. Fourth, it is work reveals design trade-offs for (i) increasing the Sc possible that differences in growth conditions change the composition of Al1−xScxN to maximize the electromechanical propensity for chemical segregation of Al and Sc, which would coupling factor, (ii) decreasing the film thickness to achieve also modulate the thermal conductivity. higher GHz-range resonance frequencies, and (iii) higher Lastly, the temperature-dependent thermal conductivity for operating temperatures resulting from higher integration two alloy compositions is plotted in Figure 5a. The thermal density and RF input powers. The thermal conductivity data conductivity has positive temperature trends until 300 K for will allow the construction of multi-physics device models that both compositions. The VCA model (based on the phonon gas fi will enable the design and development of Al1−xScxNRF lter model), on the other hand, predicts a temperature- technologies with enhanced device performance and improved independent trend above 150 K. First, it should be noted lifetime. that the experiments were performed under a temperature 43,44 rangebelowtheDebyetemperatureofAl0.8Sc0.2N. 4. EXPERIMENTAL SECTION/METHODS Therefore, the competing effects of the increase in both heat capacity and Umklapp scattering rate with temperature are 4.1. Film Thickness Measurement. Spectroscopic ellipsometry fl (Woollam M-2000F Focused Beam) was used to measure the in uencing the thermal conductivity. Second, this might fi thickness of the Al1−xScxN thin lms grown on n-type Si(100) indicate a strong thermal conductivity contribution from Ψ 52 substrates. The data were collected in the form of psi ( ) and delta highly localized modes as has been predicted for InxGa1−xAs. (Δ) functions versus wavelength at a fixed angle of incidence of 65°. Third, this trend can be influenced by the grain structure. The The three models were used for each Al1−xScxN/native SiO2/Si films studied in this work are not epitaxial (three-dimensionally structured layers, respectively. The ellipsometry measurements were oriented) but rather textured (one-dimensionally oriented). performed in air at room temperature using the wavelength range of We speculate that our model does not properly account for 300−1000 nm. 4.2. SEM Imaging. SEM was used to characterize the film phonon dispersion and scattering associated with the one- 66 dimensional nature18,54,64,65 of the columnar grains since we microstructure. Imaging was carried out in a MIRA3 (TESCAN assumed an isotropic dispersion, thermal conductivity, and USA Inc.) at a working distance of 3 mm and an accelerating voltage of 3 kV to reduce charging. The secondary electrons were collected by grain geometry. fi the Everhart-Thornley detector. The images were taken at several In summary, the thermal conductivity of Al1−xScxN lms can magnifications, providing a field of view on the sample ranging from 1 be reasonably predicted by the phonon gas model with the μ to 4 m. Within these ranges, the microstructure of ScxAl1−xN became typical alloy, boundary, and phonon−phonon scattering terms. visible, revealing an oriented grain structure. These grains were However, its anisotropic grain structure changes with thickness measured to be approximately 35 nm across all samples. Some

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∼ ﬁ Figure 7. Sensitivity plot for a 110 nm thick Al0.875Sc0.125N lm measured by (a) TDTR and (b) FDTR. In the legend, k2 and kin2 are the cross- ﬁ plane and in-plane thermal conductivities of the Al1−xScxN lm, respectively. k3 is the thermal conductivity of the Si substrate. G1 and G2 are the TBCs of the transducer/Al1−xScxN and Al1−xScxN/Si interfaces, respectively.

fi ∼ fi Figure 8. Raw data and tting results for a 110 nm thick Al0.875Sc0.125N lm measured by (a) TDTR and (b) FDTR. misoriented grains (AOGs) were observed, with lateral sizes of 50− for a particular alloy composition was approximated as a weighted 250 nm. average of the constitutive materials. Fitting of the thermal boundary 4.3. Raman Spectroscopy. Raman spectroscopy was used to conductance (TBC) (between the metal transducer and the fi characterize changes in optical phonon energies and scattering times Al1−xScxN lm) and the Al1−xScxN thermal conductivity were with scandium content. All measurements were performed at room performed simultaneously for all samples. As shown in Figure 7, the temperature using an alpha300R WiTec Raman system employing a TBC between the Sc Al − N film and the Si substrate has little impact 488 nm laser that was focused to a diffraction limited spot by a 100×/ x 1 x on the resulting Al − Sc N thermal conductivity due to the low ̅ 1 x x 0.95 NA laser in a z(x-)z scattering geometry. Raman scattered light measurement sensitivity to this parameter. Measurements were was dispersed on a 2400 g/mm grating, resulting in a spectral − performed on at least three different locations for each sample to accuracy <0.5 cm 1. To minimize laser heating of the Si substrate, a laser power of 2 mW was used and representative sampling achieved account for errors associated with the laser focusing, pump and probe μ alignment, and potential local variation of the material. The by taking 100 separate spectra evenly spaced over a 100 m linescan. fi No significant variation across the film surface was observed. Spectra uncertainty was calculated based on 95% con dence bounds for the ± providedarethecompositeaverageoftheensembleofall measurements and a 2 nm uncertainty in the metal transducer acquisitions. thickness. An identical approach for measurement, fitting, and 4.4. Thermal Conductivity Measurements (TDTR). TDTR is uncertainty analysis was used in the FDTR experiments, as described an optical pump−probe method utilizing ultrafast femtosecond laser below. pulses for measuring the temporal diffusion of heat from the surface 4.5. Thermal Conductivity Measurements (FDTR). FDTR down through the bulk over a timescale of 100−5000 ps.25 The measurements of the thermo-physical properties were carried out system used in this study is a two-color configuration with a 514 nm following deposition of an 80 nm gold (Au) transducer onto the pump beam and a 1028 nm probe beam (Flint FL2-12 by Light sample surface.26 The FDTR system uses a pump laser (λ = 405 nm) Conversion, 76 MHz repetition rate, ∼100 fs pulse width). The pump operating with a 50% duty cycle square wave to heat the Au beam is amplitude modulated via an electro-optical modulator at 7 transducer/sample, while its temperature response is captured from MHz to establish a periodic heating event that can be detected via fl λ fl fi the thermore ectance signal of a probe laser ( = 532 nm). The changes in the thermore ectance of a thin lm metal transducer at the probing wavelength was specifically chosen to maximize the surface through lock-in detection (Zurich Instruments UHFLI). Gold thermoreflectance coefficient of the Au transducer for improved (Au) thin films were deposited as transducers via electron-beam measurement sensitivity. The diameters of the focused pump and evaporation, and the thickness of the film (81.25 nm) was confirmed fl probe beams were characterized using a scanning-slit optical beam via X-ray re ection (XRR) measurements on an Al2O3 witness fi μ sample. The diameters of the focused pump and probe beams were pro ler (Thorlabs BP209-VIS) and were 15.5 and 12.4 m, characterized using a scanning-slit optical beam profiler (Thorlabs respectively. To minimize the uncertainty in the analysis of the BP209-VIS) and were 14 and 9 μm, respectively. Note that these FDTR data, the Au transducer thickness was measured by XRR. The fi beam sizes are much larger than any lateral variations in the films due Al1−xScxN lm thicknesses were determined by using variable angle to texturing or the presence of AOGs. Literature values were used for spectroscopic ellipsometry and cross-sectional SEM. Representative the thermal conductivity of Au and Si,67 as well as volumetric heat raw data and fitting results for TDTR and FDTR experiments are 68 69 44 70 capacities (CV) of Au, AlN, ScN, and Si, where the value of CV shown in Figure 8.

19038 https://doi.org/10.1021/acsami.1c02912 ACS Appl. Mater. Interfaces 2021, 13, 19031−19041 ACS Applied Materials & Interfaces www.acsami.org Research Article ■ AUTHOR INFORMATION ■ ACKNOWLEDGMENTS Corresponding Author This material is based upon work supported by the National Sukwon Choi − Department of Mechanical Engineering, The Science Foundation, as part of the Center for Dielectrics and Pennsylvania State University, University Park, Pennsylvania Piezoelectrics under grant nos. IIP-1361571, IIP-1361503, IIP- 16802, United States; orcid.org/0000-0002-3664-1542; 1841453, and IIP-1841466. This work was performed, in part, Email: [email protected] at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Authors Energy (DOE) Office of Science. G.E. would like to gratefully − Yiwen Song Department of Mechanical Engineering, The thank Sara Dickens and Joseph Michael at Sandia for Pennsylvania State University, University Park, Pennsylvania conducting EBSD analysis. Sandia National Laboratories is a 16802, United States − multimission laboratory managed and operated by the Carlos Perez Department of Mechanical Engineering, The National Technology & Engineering Solutions of Sandia, Pennsylvania State University, University Park, Pennsylvania LLC, a wholly owned subsidiary of Honeywell International, 16802, United States ’ − Inc., for the U.S. DOE s National Nuclear Security Giovanni Esteves Sandia National Laboratories, Administration under contract DE-NA-0003525. The views Albuquerque, New Mexico 87185, United States expressed in the article do not necessarily represent the views James Spencer Lundh − Department of Mechanical of the U.S. DOE or the United States Government. 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